This invention relates generally to the design of Very Large Scale Integrated Circuit (VLSI) chips, and more particularly, to a method for generating design rules in a chip layout that incorporates the effect of long-range flare in an optical micro-lithography process.
The optical micro-lithography process used in semiconductor fabrication, also known as photolithography, consists of duplicating selected circuit layout patterns onto a semiconductor wafer for an overall desired circuit performance. The desired circuit patterns are typically represented as opaque, complete and semi-transparent regions on a template commonly referred to as a photomask. In optical micro-lithography, patterns on the photo-mask template are projected onto the photo-resist coated wafer by way of optical imaging through an exposure system.
The continuous advancement of VLSI chip manufacturing technology to meet Moore's law of shrinking device dimensions in geometric progression has created several design restrictions for manufacturing semiconductor chips using optical micro-lithography process. The latter is the method of choice for chip manufacturers for the foreseeable future due to its high volume yield in manufacturing and past history of success. However, the ever shrinking device dimensions combined with the desire to enhance circuit performance in the deep sub-wavelength domain require complex design rules to ensure the desired circuit performance on a printed wafer.
A typical lithographic mask has two types of regions. They are referred to as the chrome region and the clear region. Chrome regions are opaque regions that prevent the transmission of light, whereas clear regions are transparent regions that allow the transmission of light. The pattern density of a given mask region is defined as the percentage of that region that is covered by the chrome region. The effect of flare at a particular shape on the mask due to flare emanating from all the shapes on the mask can be computed using the shape pattern density in a given region on the lithographic mask.
There are certain masks where the amount of light emanating from the mask can be controlled by changing the phase and the intensity of the light emanating from the clear or the chrome regions. In these masks, the amount of light emanating from the mask is determined by the interaction of the phase and intensity of light emitted from the chrome and the clear regions. In this type of masks, the pattern density can be defined in terms of the amount of light emanating from a given region of the mask. For this type of masks, the flare is preferably computed in terms of the pattern density.
Design rules, also referred to ‘restrictions’ embody the limitations of the optical micro-lithography process when manufacturing a chip layout. A VLSI circuit layout must obey design rules to be manufactured within the tolerance of process variation in the optical micro-lithography system. Examples of design rules are minimum width of a channel, minimum distance between two comers, minimum distance between two features, and the like. Examples of design rules are illustrated in FIG. 1.
Referring to FIG. 1, a portion of a mask layout 100 that contains several polygonal shapes is shown. Several shapes, e.g., 101 through 103 are depicted in detail at the left of the figure. More specifically, 150 represents the line width, 151 depicts the space width and 152, the corner to corner distance between the shapes. The minimum and maximum values of 151 through 152 are determined by the specifications of the design rules.
A VLSI circuit consists of several layers overlaid on top of one another. The chip operates properly only if each of the layers operates properly. Each layer is manufactured using an optical lithography process that is suited for the particular layer. For each layer, a set of design rules is generated by process engineers, considering the limitations of the particular optical micro-lithography process used. Designers of the VLSI circuit ensure that the circuit, while it is designed, obeys the stated rules. Finally, the circuit is tested by way of a Design Rule Checker (DRC) for any violations of the design rules before it is handed over to manufacturing.
The aforementioned methodology is illustrated in FIG. 2. In step 201, the critical dimensions and the pitches of the shapes are decided upon based on the technology. By way of example, the current state of the art technology that is presently manufactured, require a 90 nm gate width. The circuit consists of several layers of materials. The bottom most layers in a typical VLSI circuit consists of a large number of transistors. The transistors are made of at least two layers. These are, in turn, connected to one another by several layers of metal interconnects. Each layer of metal is interconnected by via layers. In step 202, the number of layers for the circuit to be manufactured is determined. Each layer has its own critical dimensions and pitches, which are decided in step 203. These dimensions in turn depend on the critical dimensions of the circuit, as specified in step 201. Since each layer is fabricated in a predetermined order, the manufacturing process must also decide on the lithographic process to be used for each layer (step 204). In step 205, any limitation of the lithographic process for each layer is determined, and is followed by step 206, wherein the number of masks for each layer is defined. Usually, each layer requires simple chrome on a glass mask. However, occasionally, a layer can be manufactured using two or more masks. In step 207, the design-rules to be applied on the design for each mask are determined on the basis of the optical lithographic process. In step 208, the masks are designed in accordance with the prescribed design rules. In step 209, the masks are checked for violations of design rules before their release to manufacturing.
There are two major objectives that the design rules must satisfy. First, the design rules must not be overly restrictive, since overly restrictive design rules reduce the circuit performance. By way of example, if the specified minimum feature width within the design rule that is required for the circuit to function at a pre-specified speed is overly restrictive, then the circuit will, as a result, underperform.
Secondly, the design rules must ensure that the circuit to be manufactured remains within the tolerance of the process variation. Optical micro-lithography processes are subject to several variations. The yield of the process decreases drastically if the chip cannot be manufactured under these variations, making the manufacturing economically unattractive. Often these two objectives cannot be mutually satisfied. Accordingly, design rules are generated to balance the above two objectives.
In the current state of the art, the limitations of the optical micro-lithography process that are embodied in the design rules are caused by diffractions of light in the optical system and the ensuing chemical effect in the resist development process.
The success of the generating appropriate design rules under the two conflicting objectives often depends on the use of a highly accurate simulator to predict the lithographic processing effects on selected points on the mask shapes which, ultimately, are printed on the wafer. Based on the simulation, a modeled integrated circuit layout determines the overall printed image on the wafer by interpolating selected simulated points.
Aerial image simulators that compute the images generated by optical projection systems have proven to be a valuable tool for analyzing and improving state of the art optical lithography systems. These simulators have found wide application in advanced mask designs. Modeling aerial imaging is a crucial component of semiconductor manufacturing. The aerial image generated by the mask, i.e., the light intensity of an optical projection system image plane, is a critically important parameter in micro-lithography for governing how well a developed photo-resist structure replicates a mask design and which, generally, needs to be computed to an accuracy greater than 1%.
In the prior art, simulated physical effects include only the diffraction of light in the presence of low order aberrations, limiting the accuracy of the predictions. Practitioners of the art will readily recognize that physical effects may include all effects of mask processing such as optical, x-ray, chemical, etching and extreme ultra-violet ray processing.
A significant effect not currently included is the scattered light which affects the exposure over long distances on the wafer. Such long-range optical effects are generally referred to as “flare” in the literature. Given the current extremely tight requirements on Across-Chip-Line-Width-Variation (ACLV), flare effects need to be included. Also, in some cases, novel RET methods such as alternating Phase Shifting Masks (Alt-PSM) can exacerbate the problem by requiring dual exposure. The problem is even more pronounced in bright field masks that are used in printing critical levels and which control the ultimate performance of the circuit, such as gate and diffusion levels.
Accuracy is of critical importance in the computation of calibrated optical or resist models. The accuracy in the simulation of wafer shapes is necessary to gain a better understanding and provide an improved evaluation of the OPC methodologies. Through analytical processes, fidelity in the wafer shapes to the “as intended” shapes ultimately achieve a better correction of the mask shapes. An increase in yield at chip manufacturing is a direct consequence of achieving this accuracy.
A significant difficulty when taking into consideration long range effects, such as flare, is the extent of the corrections flare effects required on the mask. In the prior art, optical lens aberrations are modeled by just the 37 lowest order Zernikes and, therefore, only aberrations that deviate light by 1 micron or less are included. The effect of aberrations dies off within that range. The flare effect, on the other hand, extends up to a few mms, thus covering the entire chip area. Current Model-Based OPC (MBOPC) software tools are not equipped to handle such long distance effects.
The limitations of the current methodology are shown in FIG. 3. Therein is illustrated the extent of the flare kernel and the power spectral density of the flare accounting for the optical energy falling on the exposed mask, which is plotted against the logarithmic distance from the mask opening. The distance is measured in terms of the number of wave cycles/pupil or the distance x/(λ/2*NA), wherein λ is the wavelength of the light and NA, the numerical aperture. The limitations of the current art which are modeled by the 37 Zernike polynomial parameters Z4 through Z37 are shown in 301. On the other hand, the actual extent of the flare is shown in 304. The flare can be modeled by the Power Law F(x)=K/(x−x′)γ/2, wherein the constant γ ranges from 1.5 to 3, depending on the optical system used in the lithographic process. The non-optimal interferometers used to measure the extent of flare are shown in 302. The non-optimal interferometer grossly underestimates the energy of the flare. On the other hand, a regular interferometer can be used to find the extent of the flare, as shown in 303.
In current MBOPC tools, interaction regions are in the order of 1 micron. Any increase in size of that region significantly affects the timing and accuracy of the simulation and, consequently, affects the OPC results. As a result, the need for fast and accurate flare modeling is being felt throughout the industry.
It has been shown through experimental data that the effect of flare on the variation of the Critical Dimension (CD) of transistors and other circuit devices can be as high as 6% of the designed dimensions for certain optical lithography process configurations. Therefore, it is imperative that these effects be considered in the simulation tools used by the MBOPC software.
The experimental justification of flare is shown in FIG. 4. Therein, the same mask structure printed on several locations on the wafer is shown having three different neighborhood background transmissions. Measured CDs of different wafer site locations are plotted against different background transmissions. The CD with 6%, 50% and 100% neighborhood background transmissions are shown in 401, 402 and 403, respectively. It is observed that a CD having a 6% neighborhood background transmission shows more pronounced CD variations than other plots.
In the prior art, the following mathematical treatment in the optical proximity correction engine is commonly used. These approaches are in one form or another, related to the Sum of Coherent Source (SOCS) method, which is an algorithm for efficient calculation of the bilinear transform.
Sum of Coherent Systems (SOCS) Method
The image intensity is given by the partially coherent Hopkin's equation (a bilinear transform):I0({right arrow over (r)})=∫∫∫∫d{right arrow over (r)}′dr″h({right arrow over (r)}−{right arrow over (r)}′)h*({right arrow over (r)}−r″)j({right arrow over (r)}′−r″)m({right arrow over (r)}′)m*({right arrow over (r)}″),where,                h is the lens point spread function (PSF);        j is the coherence;        m is the mask; and        I0 is the aerial image.        
By using the SOCS technique, the optimal nth order coherent approximation to the partially coherent Hopkin's equation can be expressed as
            I      0        ⁡          (              r        →            )        ≅            ∑              k        =        1            n        ⁢                  λ        k            ⁢                                                            (                              m                ⊗                                  ϕ                  k                                            )                        ⁢                          (              x              )                                                2            where λk, φk({right arrow over (r)}) represents the eigenvalues and eigenvectors derived from the Mercer expansion of:
            W      ⁡              (                                            r              →                        ′                    ,                      r            ′′                          )              =                            h          ⁡                      (                                          r                _                            ′                        )                          ⁢        h        *                  (                      r            ′′                    )                ⁢                  j          ⁡                      (                                                            r                  →                                ′                            -                              r                ′′                                      )                              =                        ∑                      k            =            1                    ∞                ⁢                              λ            k                    ⁢                                    ϕ              k                        ⁡                          (                                                r                  →                                ′                            )                                ⁢                                    ϕ              k                        ⁡                          (                                                r                  →                                ′′                            )                                            ,suggesting that a partially coherent imaging problem can be optimally approximated by a finite summation of coherent imaging, such as linear convolution.
SOCS With Pupil Phase Error
The above calculation assumes an ideal imaging system. However, when a lens aberration is present, such as the pupil phase error and apodization, one must include the pupil function:h({right arrow over (r)})=∫∫P({right arrow over (ρ)})exp(i W({right arrow over (ρ)}))exp(i2π{right arrow over (r)}·{right arrow over (ρ)})d2{right arrow over (ρ)}where,
P({right arrow over (ρ)}) is the pupil transmission function, and W({right arrow over (ρ)}) is the pupil phase function, which contains both aberration and flare information.
Because of a possible higher spatial frequency in the wavefront function, h({right arrow over (r)}) will have a larger spatial extent. In this case, the number of eigenvalues and eigenvectors required are higher than those of an ideal system. Hence, the kernel support area is extended to take into account the contribution from a distance greater than λ/NA. However, the basic mathematical structure and algorithm remains the same.
Physical Model of Flare
Flare is generally considered to be an undesired image component generated by high frequency phase “ripples” in the wavefront corresponding to the optical process. Flare thus arises when light is forward scattered by appreciable angles due to phase irregularities in the lens. An additional component of flare arises from a two-fold process of backscatter followed by re-scatter in the forward direction, as will be discussed hereinafter. High frequency wavefront irregularities are often neglected for three reasons. First, the wavefront data is sometimes taken with a low-resolution interferometer. Moreover, it may be reconstructed using an algorithm of an even lower resolution. Secondly, even when the power spectrum of the wavefront is known or inferred, it is not possible to include the effect of high frequency wavefront components on an image integral that is truncated at a short ROI (region of interaction) distance, causing most of the scattered light to be neglected. Finally, it is not straightforward to include these terms in the calculated image. The present invention addresses these problems.
Flare also arises from multiple reflections between the surfaces of the lens elements (including stray reflections from the mask and wafer). The extra path length followed by this kind of stray light usually exceeds the coherence length of the source, which means that ordinary interferometric instruments will not detect it. Thus, as with a wavefront ripple, flare from multiple reflections is not considered in the prior art OPC. The reasons are similar, i.e., stray reflections require extra effort to detect, they are largely generated outside the ROI, and their contribution to the image is not handled by conventional algorithms of lithographic image simulation.
Stray reflections are dim, and generally represent an acceptable loss in image intensity. Thus, stray reflections are not particularly deleterious unless they actually illuminate the wafer with stray light. For this to occur, it is usually necessary for two surfaces to participate in the stray light path, one surface to back-reflect a small portion of the primary imaging beam, and another to redirect some of the stray reflection forward towards the wafer. In nearly all cases, this light is strongly out of focus, and amounts to a pure background. In contrast, stray image light which is reflected back from the wafer and then forwarded from the underside of the mask remains reasonably well imaged at the wafer itself. For this reason, light in the primary image which is back-reflected along this particular path (wafer to mask, and back to the wafer) is usually not counted as stray light (particularly if, as is usually the case, the twice-through beam is weak compared to the direct image). In contrast, light following other stray paths will form a defocused background at the wafer. Such an unpatterned background has a non-negligible impact even at a 1% level.
Nowadays the reflectivity of the mask and wafer are held well below 100% (typically, an order of magnitude lower), but residual mask and wafer reflectivity are themselves typically an order of magnitude greater than the residual reflectivities of the lens element surfaces (which can be made highly transmissive). Nonetheless, the cumulative impact of all stray reflection paths which involves two successive stray reflections from lens surfaces are roughly comparable to the cumulative impact of those paths which involves only a single lens reflection (together with a single reflection from the mask or the wafer). This heightened cumulative impact is simply the result of the large number of lens surfaces (e.g., about 50) that are present in state of the art lithography lenses.
In principle, stray reflections do the most damage if focused or almost focused at the primary image plane, but in practice, this instance (unlikely to begin with) is checked for and avoided by lens designers. Stray reflections thus tend to be defocused for large distances, i.e., distances corresponding to the macroscopic scale of characteristic lens dimensions. As a result, the flare kernel from stray reflections is significantly flat on the scale of lens resolution, or even on the scale of typical flare measurement patterns. This behavior allows the contributions to the flare kernel from stray reflections and wavefront ripple to be distinguished from one another, since the latter falls off quite rapidly at distances larger than the lens resolution, e.g., as the inverse second or third power of distance, while the former falls off only slowly.
However, the contribution of the stray reflection is effectively constant over approximately 500 mm scale of the measurement site.
It is generally observed that the flare energy from a wavefront ripple follows approximately the inverse power law relationship given by: F(x)=K/(x−x′)γ. This is shown in FIG. 5. Therein, the extent of flare is plotted in curve 501 for a typical optical process of a numerical aperture (NA) of 0.75 and a pupil size (σ) of 0.3. Under this condition, the power law shows γ=1.85.
Conventionally, design rule for mask design is derived from consideration of short range optical interaction due to diffraction of light. These rules only deal with edges within a certain optical radius, typically smaller than 1 um from the pattern edge in consideration. However flare is long range in nature (>>1 μm) and contribution from a large distance away is significant. Such a rule will depend on the local pattern density around the edge in consideration. The random pattern density across the full chip will cause additional ACLV error.
Currently, there is no systematic and scientific approach in the current art on how to quantify the effect of flare into devising a rule for the designer to follow under the assumption that any design scenario can happen in any full chip design. Also, currently there are no available tools for generating design rules incorporating flare effects, and there are no know publications to that effect. The present invention satisfies the need for generating design rules which accurately incorporates the effect of flare.
In patent application Ser. No. 10/844,794 of common assignee, which is herein incorporated by reference, a method of performing an optical proximity correction (OPC) using flare is described. This approach is based on computing the image intensity at a predetermined point having both diffraction and flare based intensities. However, this methodology is applicable only after a mask design is made and is computationally very expensive.